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Solve Systems of Equations by Substitution: example 5.14 · Physics Playground

Exercises Systems of equations

Example 5.14 from Elementary Algebra, 5.2 Solve Systems of Equations by Substitution

Solve Systems of Equations by Substitution: example 5.14

Solve the system by substitution.

${\begin{matrix} x + y = −1 \\ y = x + 5 \end{matrix}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

The second equation is already solved for y. We will substitute the expression in place of y in the first equation.


The second equation is already solved for y. We will substitute into the first equation.
Replace the y with x + 5.
Solve the resulting equation for x.


Substitute x = −3 into y = x + 5 to find y.

The ordered pair is (−3, 2).
Check the ordered pair in both equations: $\begin{matrix} \begin{matrix} x + y & = & - 1 \\ - 3 + 2 & \overset{?}{=} & - 1 \\ - 1 & = & - 1 ✓ \end{matrix} & \begin{matrix} y & = & x + 5 \\ 2 & \overset{?}{=} & - 3 + 5 \\ 2 & = & 2 ✓ \end{matrix} \end{matrix}$
	The solution is (−3, 2).

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the system by substitution. ${\begin{matrix} x + y = 6 \\ y = 3 x - 2 \end{matrix}$

How did it go?

PreviousSolve Systems of Equations by Substitution: example 5.13 Next Solve Systems of Equations by Substitution: example 5.15

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 5.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.